Half Subtractor | Truth table & Logic Diagram

A Subtractor is a digital logic circuit in electronics that performs the operation of subtraction of two number. Subtractors are classified into two types: half subtractor and full subtractor. The half subtractor (HS) circuit has two inputs: A and B, which subtract two input binary digits and generate two binary outputs i.e. borrow and difference.

half-subtractor-block-diagram
Fig. 1 Half subtractor block diagram

Truth table of half subtractor

The truth table of the HS Circuit is shown in figure 2.

half-subtractor-truth-table
Fig. 2 Truth table

Implementation of HS

Logical expression for difference,

Logical expression for borrow,

half-subtractor-logic-diagram
Fig. 3 Logic Diagram

The HS works by combining the operations of basic logic gates, with the simplest form using only an XOR, one NOT and an AND gate.

Note:

1. Minimum number of NAND Gate required implementing HS = 5

2. Minimum number of NOR Gate required implementing HS = 5

3. Number of Multiplexers required implementing HS = 3    (2×1 Multiplexer)

4. HS can be implemented by a combination of one 2×4 decoder and one OR gate.

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